Detection of edges of noisy images by 1-D and 2-D linear FIR digital filters

Several image edge detection algorithms are developed by means of low-order 1-D and 2-D finite impulse response (FIR) filters. The filters obtained are linear and shift-invariant, and can be implemented efficiently by discrete convolution or discrete Fourier transform. The FIR edge detectors are designed such that they have the ability to differentiate the edges and to smooth the noises in a noisy image simultaneously. The proposed first-order FIR differentiators, as compared with conventional gradient operators proposed by Prewitt, Sobel, Isotropic, etc., are much less sensitive to noise; and the proposed second-order FIR differentiators ARE COMPUTATIONALLY more efficient than the popular Laplacian of Gaussian method. The edge maps of noisy images obtained from the proposed first-order FIR edge detectors (1-D or 2-D) are compared with those obtained from the commonly used Sobel operator. The comparison shows that the former is much better than the latter. The comparison between the proposed second-order FIR edge detector and the Laplacian of Gaussian leads to a similar conclusion. Less computation time is necessary for the implementation of the proposed second-order FIR edge detector than that of the Laplacian of Gaussian